Aktuelle Entwicklungen in der Theorie II
Gitter-Eichtheorie
Hartmut WittigInstitut für Kernphysik und Helmholtz Institut Mainz
KHuK Jahrestagung30. November 2012
2 | Overview
Overview
I. Nucleon properties from lattice QCD
II. Resonances and scattering
III. Hadronic contributions to the muon
IV. QCD Thermodynamics
V. Ab initio nuclear physics
3 | Nucleon Properties from Lattice QCD
I. Nucleon Properties
4 | Nucleon properties from lattice QCD
Nucleon properties from lattice QCD
Nucleon form factors, charge radii and axial charge
Average momentum fraction
Nucleon mass and sigma term
Strangeness in the nucleon
Achieve fullcontrol oversystematicerrors
Provide stablelattice estimate
5 | Nucleon properties from lattice QCD
Nucleon form factors and axial charge
Experimental dependence and charge radii not reproduced
Lattice simulations underestimate axial charge
Systematic effects not fully controlled Lattice artefacts
Chiral extrapolation to physical pion mass
Finite-volume effects
“Contamination” from excited states
Determine form factors from ratios of three- and two-point functions,
Source-sink separation fm due to bad signal/noise ratio
6 | Nucleon properties from lattice QCD
Nucleon form factors and axial charge
Correlator ratio:
Summed insertion:
𝑆 ( 𝑡 𝑠 )≡∑𝑡=0
𝑡 𝑠
𝑅𝐴 (𝑡 , 𝑡 𝑠 )=𝑐+𝑡𝑠 {𝑔 Abare+𝑂 (𝑒−Δ 𝑡 𝑠 )}
7 | Nucleon properties from lattice QCD
Nucleon form factors and axial charge
flavours of improved Wilson fermions;
MeV, , fm
[Capitani, Della Morte, von Hippel, Jäger, Jüttner, Knippschild, Meyer, H.W., Phys Rev D86 (2012) 074502]
𝑔 A=1.223±0.063stat❑ ¿¿
flavours of improved Wilson fermions;
MeV, , fm
8 | Nucleon properties from lattice QCD
Nucleon form factors and axial charge[Capitani, Della Morte, von Hippel, Jäger, Knippschild, Meyer, Rae, H.W., arXiv:1211.1282]
9 | Nucleon properties from lattice QCD
Moments of parton distribution functions
Average momentum of unpolarised iso-vector PDF:
⟨𝑥 ⟩𝑢−𝑑=∫0
1
𝑑𝑥 𝑥 {𝑢 (𝑥 )+𝑢 (𝑥 )−𝑑 (𝑥 )−𝑑 (𝑥 ) }
Cannot reconcile lattice and phenomenological estimates for [Alekhin, Blümlein, Moch, Phys Rev D86 (2012) 054009]
Excited state contamination cannot explain discrepancy
Strong pion mass dependence?
10 | Nucleon properties from lattice QCD
Moments of parton distribution functions[QCDSF Collaboration, Bali et al., Phys Rev D86 (2012) 054504]
flavours of improved Wilson fermions;
MeV, 74, fm
at
11 | Nucleon properties from lattice QCD
Strangeness contribution to the proton spin12ΔΣ+𝐿𝑞+Δ𝐺=
12, ΔΣ=Δ𝑢+Δ𝑑+Δ 𝑠+…
Inconclusive results for
Lattice calculations of involve calculation of quark-disconnected diagrams
Stochastic methods: “stochastic” versus “gauge” noise
12 | Nucleon properties from lattice QCD
[QCDSF Collaboration, Bali et al., Phys Rev Lett 108 (2012) 222001]
flavours of improved Wilson fermions;
MeV, , fm
Strangeness contribution to the proton spin
Non-singlet renormalisation factor:
Δ𝑞MS (𝜇)=𝑍 Ans (1+𝑏 A𝑎𝑚q ) Δ𝑞bare+ 1
2z (𝜇 ) (Δ𝑢+Δ𝑑)bare
Results:
( scheme, )
(No continuum limit, no chiral extrapolation, quenched strange quark)
13 | Resonances and Scattering
II. Resonances and Scattering
14 | Nucleon properties from lattice QCD
Mathematically exact formalism in the one-channel case
Resonances in Lattice QCD
Resonances mostly treated naïvely in lattice QCD: Lüscher formalism: extract resonance parameters from finite-size scaling
of multi-hadron states in a box
Signature for resonance: avoided level crossing, e.g. for
15 | Nucleon properties from lattice QCD
πK scattering and the κ(800) resonance[Döring and Meissner, JHEP 1201 (2012) 009]
broad resonance; avoided level crossing washed out Two decay channels: and Use infinite-volume methods to predict finite-volume energy levels, as a
guide for future lattice simulations
1. Perform global fit to meson-meson PW data pole and width of 2. Use solution to generate pseudo (lattice) data3. Analyse data in terms of fit potential with LO chiral interaction constraints
Obtain scattering phases and pole position from extended Lüscher method
16 | Nucleon properties from lattice QCD
Scattering processes off charmed mesons[Liu, Orginos, Guo, Hanhart and Meissner, arXiv:1208.4535]
Compute scattering lengths of and in lattice QCD Chiral fits based on unitarised ChPT: determine 5 LECs plus one
parameter of UChPT
Values of LECs allow for predictions in other channels:
Results support interpretation of the as a molecule
Prediction for isospin breaking strong decay width:
17 | Hadronic contributions to the muon
III. Hadronic contributions tothe muon
18 |Hadronic contributions to the muon
Hadronic vacuum polarisation contribution
𝑎𝜇VP;had=(690.75±4.75) ∙10−10
(combined data)
Theory prediction uses experimental data as input Ab initio estimate from Lattice QCD: total accuracy of required!
19 | Hadronic contributions to the muon
Hadronic vacuum polarisation contribution
Convolution function peaked far below lowest Fourier momentum Quark-disconnected diagrams contribute
Lattice approach: evaluate convolution integral over Euclidean momenta
20 | Hadronic contributions to the muon
Hadronic vacuum polarisation contribution
Current lattice estimates not competitive with dispersive approach:
Improve statistical accuracy Simulate at the physical pion
mass Include quark-disconnected
diagrams
21 | Hadronic contributions to the muon
Hadronic vacuum polarisation contribution
Apply twisted boundary conditions to reach lower momenta
New ensembles: MeV, , fm
[Della Morte, Jäger, Jüttner, H.W., JHEP 1203 (2012) 055, and to appear]
22 | Hadronic contributions to the muon
Lattice calculations versus dispersion relations
Relation between vacuum polarisation and -ratio in the Euclidean domain:
[Bernecker, Meyer, EPJA 47 (2011) 148, and in preparation]
Lattice calculations yield Use parameterisation of measured and evaluate the integral
23 | QCD Thermodynamics
IV. QCD Thermodynamics
24 | QCD Thermodynamics
Freeze-out conditions in heavy-ion collisions
RHIC energy scan: measure fluctuations of conserved charges:
Net baryon number (B), electric charge (C), Strangeness (S)
Fluctuations provide information on hadronisation:
Freeze-out curve:
Evaluate cumulants of net charge fluctuations as a function of and
𝑅𝑚 ,𝑛𝑋 ≡
𝜒𝑚 ,𝜇𝑋
𝜒𝑛 ,𝜇𝑋 , 𝑋=𝐵 ,𝑄
Initial condition:
Can measure experimentally
Can compute in Hadron Resonance Gas model and Lattice QCD
25 | Nucleon properties from lattice QCD
Freeze-out conditions in heavy-ion collisions
flavours of improved staggered quarks (“HISQ”);
MeV, lattice sizes and
Compute charge densities and fluctuations via Taylor expansion
[BNL-Bielefeld Collaboration, Bazavov et al., Phys Rev Lett 109 (2012) 192302]
Lattice simulation yields prediction for -dependence of
STAR Collab. (preliminary)
26 | Ab initio nuclear physics
V. Ab initio Nuclear Physics
27 | Ab initio nuclear physics
The Hoyle state from first principles
Hoyle state: excited state of 12 above the 8 4 threshold
Important catalyst in the CNO nuclear cycle
Hoyle state decays electromagnetically into then into
Investigate spectrum and structure of triple-alpha systems via
Monte Carlo simulations of chiral effective field theory
Include terms up to NNLO, i.e.
[Epelbaum, Krebs, Lee, Meissner,… ]
28 | Ab initio nuclear physics
The Hoyle state from first principles[Epelbaum, Krebs, Lee, Meissner, Phys Rev Lett 106 (2012) 192501]
Compute projection amplitude of quantum state on periodic lattice
Spectrum of 12
Theory (NNLO)
Experiment
Good agreement with experiment; consistent two- and three-body forces must be included
Anthropic test: how sensitive is the triple-α process against small modifications in QED and QCD?
29 | Ab initio nuclear physics
The Hoyle state from first principles[Epelbaum, Krebs, Lähde, Lee, Meissner, arXiv:1208.1328 ]
Compute projection amplitude of quantum state on periodic lattice
Extract information on the structure by preparing different initial states:
Successive creation of 4 nucleons Clusters of alpha-particle
“bent arm” configurationPreferred by Hoyle state
Precision Physics, Fundamental Interactionsand Structure of Matter
Cluster of Excellence:
Hartmut WittigInstitute for Nuclear Physics
Matthias NeubertInstitute for Physics
Spokespersons:
31 | The PRISMA Cluster of Excellence
Approx. 3 programmes p.a., each lasting 3-8 weeks, combined with a topical workshop
Co-organised by a team of external scientists and local researchers
Applications evaluated by International Advisory Board
Additional 2 schools over the 5-year funding period, lasting 2-3 weeks each
Scientific Programmes, Workshops and Schools:
MITP Programs in 2013:
Low-energy precision physics external organisers: K. Kumar, M. Ramsey-Musolf local organisers: H. Meyer, H. Spiesberger
The first three years of the LHC external organisers: M. Carena, T. Plehnlocal organisers: B. Jäger, M. Neubert
Mainz Institute for Theoretical Physics (MITP)
Call for Proposals for 2014
Nima Arkani-Hamed Marcela CarenaMichael CreutzGian GiudiceWilliam MarcianoNeal Weiner
Manfred LindnerJan LouisDirk KreimerChristof WetterichMartin SavageDieter Zeppenfeld